When two linear equations are plotted on a coordinate plane, their intersection point represents the solution to the system of equations. This solution is the set of values for the variables (typically $x$ and $y$) that satisfy both equations simultaneously.

Key Points:

1. Linear Equations: These are equations of the form $ax + by = c$, where $a$, $b$, and $c$ are constants, and $x$ and $y$ are variables.
2. Graphing: Each equation can be represented as a straight line on the coordinate plane. The solution to the system is the point where the two lines intersect.
3. Intersection: The coordinates of the intersection point are the values of $x$ and $y$ that make both equations true. This is the only solution if the lines are not parallel (in the case of consistent, independent equations).

For example, if you have the following system of equations: $y = 2x + 3$ $y = -x + 1$ You would graph both equations, and the point where the two lines cross gives you the solution.

Solving the System Algebraically:

You can also solve for $x$ and $y$ algebraically using substitution or elimination methods to find the point of intersection.

Would you like to see a detailed solution to a system of equations or learn about a specific method for solving these?

Related Questions:

1. How do you solve a system of linear equations using substitution?
2. What is the significance of parallel lines in a system of linear equations?
3. How can you graph a system of equations using software or a calculator?
4. What happens when two lines are coincident in a system of equations?
5. How do you determine if a system has no solution, one solution, or infinitely many solutions?

Tip: When graphing, ensure that both lines are plotted accurately by using enough points on the grid, and check the scales on both axes.